Filter network and method

ABSTRACT

A filter network and method for the rejection of all but a selected band of frequency, the apparatus and method utilizing a pair of notch-type filters such as twin-T filters, with a common input connection and separate outputs connected to different inputs on a differential amplifier.

United States Patent Inventor Appl. N 0. Filed Patented Assignee FILTERNETWORK AND METHOD 1 Claim, 6'Drawing Figs.

US. Cl 330/30, 330/31, 333/75 Int. Cl 1103f 3/68, H03h 7/10 Field ofSearch 330/30, 30 (D),69, 126, 21, 31; 333/75; 329/140 PrimaryExaminer.lohn Kominski Assistant Examiner-Lawrence J. Dahl Attomeys-LewSchwartz and Donald R. Stone ABSTRACT: A filter network and method forthe rejection of all but a selected band of frequency, the apparatus andmethod utilizing a pair of notchtype filters such as twin-T filters,with a common input connection and separate outputs connected todifferent inputs on a differential amplifier.

DIFF AMP.

Patented May 18, 1971 FILTER 10 20 16 DIFF AMP TWIN T FIE! 14 FILTER 610 1 OUTPUT SSEIPAUGTE VOLT' J7 MAGNiTUDE Er.

2 x 3 x y FREQUENCY FREQUENCY F15 5 PIES OUTPUT VOLT.

FREQUENCY f REQUENCY Z FIE5 i o 40 7 72 /81 82 t 20 INVEN'IOR. (08521KAA/nmsazr B Y BACKGROUND OF THE INVENTION The apparatus and method ofthis invention relate generally to filter networks, and morespecifically to a filter network for accurately rejecting all but aselected band of frequencies. Filter networks are well known in the art,and have many and varied uses. One problem that has arisen in variouselectrical circuits is the need for a network that will pass signals ofa preselected frequency band, while rejecting comparatively large inputsof adjacent frequencies. Prior art attempts to achieve the desirednetwork response by using a tuned passive network or a tuned acfiveamplifier, that is, an amplifier with a feedback loop including a notchfilter network, have met with problems of inadequate frequencydiscrimination or instability (e.g., ringing) with large magnitudeinputs. It is believed that the problems of proper damping are too acutefor any prior known solution, as either over or under damping results inundesirable situations.

SUMMARY OF THE INVENTION Briefly described, the apparatus and method ofthis invention provide a solution to the above-mentioned problems byusing a pair of passive notch filters, such as twin-T filters, whichhave their inputs connected to a common point adapted to receive acommon input signal. Each output of the two filters is connected to adifferent input on a differential amplifier. The filters are tuned todifferent frequencies, one near the upper and one near the lowerfrequency of the band it is desired to pass, as will be more fullydescribed below.

The filters have complex impedances which vary as a func' tion offrequency of the applied input signal and which are substantiallyidentical over the entire frequency spectrum except for a. narrowfrequency range from slightly below the lower resonant frequency toslightly above the upper resonant frequency. Throughout that frequencyrange, the complex impedances of the two filters are different therebyproducing different complex output voltages for a common input signalwhich results in an output signal from the differential amplifi' er. Toachieve a relatively large output signal from the network throughout theentire frequency range between the two resonant frequencies and stillhave relatively sharp cutofi's to the passband when bootstrapped twin-Tfilters are used, the upper resonant frequency must be not more thanapproximately twice the lower resonant frequency. When less sharpcutoffs to the passband can be tolerated, a relatively large output canbe obtained throughout a band in which one resonant frequency is morethan twice the other by properly skewing one or both of the filterresponse curves.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 discloses a block diagram ofthe apparatus of this invention;

FIG. 2 is a schematic drawing of the apparatus shown in the blockdiagram of FIG. 1, comprising a preferred embodiment of the apparatus ofthis invention;

FIG. 3 is a-graph denoting the output voltage magnitude, as a functionof frequency, of each of the filters shown in FIGS. 1 and 2 for aconstant voltage input;

FIG. 4 is a graph denoting the output voltage phase angle, as a functionof frequency, of each of the filters of FIGS. 1 and 2 for a constantvoltage input;

FIG. 5 is a graph denoting a general output voltage magnitude curve fromthe differential amplifier of FIG. I for a constant magnitude inputsignal to the notch filters as a function of frequency; and

FIG. 6 is a graph of a specific output voltage magnitude curve from thedifferential amplifier of FIG. 2, with properly chosen components, for aconstant magnitude input signal to the notch filters as a function offrequency.

2 DESCRIPTION OF THE PREFERRED EMBODIMENT Referring first to FIG. 1there is shown, in block diagram form, a pair of notch filters l0 and11, indicated as being twin- T filters. Filter 10 has an input terminal12 and an output terminal 13. Filter 11 has an input terminal 14 and anoutput terminal 15. Input terminals 12 and 14 are connected to a signalinput terminal 16, adapted to receive an electrical signal. Filters l0and 11 are tuned to different resonant frequencies.

Also shown in FIG. 1 is a differential amplifier 17, having a pair ofinput terminals 18 and 19 and an output terminal 20. Output terminal 13of filter 10 is connected to input terminal 18 of amplifier 17. Outputterminal 15 of filter 11 is connected to input terminal 19 of amplifier17. Therefore, in operation, an electrical signal appearing at signalinput terminal 16 will be felt at input terminals 12 and 14 to be actedon by filters 10 and 11. The resulting output of filters 10 and 11 willbe felt across input terminals 18 and 19 of amplifier l7, and where thetwo outputs vary sufficiently to be detected by differential amplifier17, the final resulting output will appear at terminal 20. Thisoperation will be more fully described below.

Referring now to FIG. 2, there is shown a schematic diagram of apreferred embodiment of the apparatus of this invention. A first twin-Tfilter, comparable to filter 10 of FIG. 1, is shown comprising aserially connected pair of resistors 31 and 32 connected in parallelwith a serially connected pair of capacitors 33 and 34. A capacitor 35and a variable resistor 36 are shown serially connected between ajunction 37 and a junction 38. Junction 37 is a point between resistors31 and 32, while junction 38 is a point between capacitors 33 and 34. Ajunction 41 between resistor 32 and capacitor 34 is connected through aresistor 46 to a ground bus 44. There is also shown a field efiecttransistor 40 having its gate electrode connected to junction 41, itssource electrode connected through a resistor 43 to bus 44, and to ajunction 42 between capacitor 35 and variable resistor 36, and its drainelectrode connected to a positive bus 45.

In FIG. 2 there is also shown a second twin-T filter comparable to blockll of FIG. 1 and comprising a pair of serially connected resistors 51and 52 which are connected in parallel across a pair of seriallyconnected capacitors 53 and 54. A capacitor 55 and a variable resistor56 are connected between a junction 57 and a junction 58. Junction 57 isbetween resistors 51 and 52, while junction 58 is between capacitors 53and 54. A junction 61 between resistor 52 and capacitor 54 is connectedthrough a resistor 66 to negative bus 44. There is also shown a fieldefiect transistor 60 having its gate electrode connected to junction 61,its source electrode connected through a resistor 63 to bus 44 and to ajunction 62 between capacitor 55 and variable resistor 57, and its drainelectrode connected to positive bus 45.

A junction 21 between resistor 31 and capacitor 33, and a junction 22between resistor 51 and. capacitor 53, are connected to signal inputterminal 16.

There is also shown a differential amplifier comparable to amplifier 17of FIG. I, and comprising a pair of transistors 70 and 80, here shown asNPN transistors. The emitter electrodes of both transistors 70and 80 areconnected through a resistor to negative bus 44. The collector electrodeof transistor 70 is connected through a resistor 71 to positive bus 45,and the collector electrode of transistor is connected through aresistor 31 to positive bus 45. The base electrode of transistor 70 isconnected through a resistor 72 to bus 45, and through a resistor 73 tonegative bus 44. The base electrode of transistor 80 is connectedthrough a resistor 82 to bus 45, and through a resistor 83 to negativebus 44. The collector electrode of transistor 80 is shown connected tooutput terminal 20 of the differential amplifier such as 17 in FIG. 1.The source electrode of field effect transistor 40 is connected througha capacitor 68 to the base electrode of transistor 70. The sourceelectrode of field effect transistor 60 is connected through a capacitor69 to the base electrode of transistor 80.

To best understand the operation of the apparatus of FIGS. 1 and 2, thegraphs of FIGS. 3, 4 and 5 should first be explained. In FIG. 3, thereis shown in solid lines a graph of the output voltage magnitude responseto constant magnitude input signals of filter W of FIG. I, while theresponse of filter i1 is shown in dotted lines. The graph is shown on anabscissa representing increasing frequency, and an ordinate representingincreasing voltage. From the graph of FIG. 3 it will be apparent thatfor frequencies below that denoted X on the graph, the complex impedanceof filter 10 is nearly constant and its output voltage will remain 2,,until the frequency approaches the resonant frequency X at which timethe complex impedance of filter lit) begins changing and a sharp peak ornotch output will lower the tuned filter 10 output to voltage e However,as the frequency increases beyond the resonant frequency X of filter 10,the complex impedance returns to its original constant value and theoutput will again return to volt age level e,. The same is true forfilter 11, except that it is tuned to a resonant frequency Y, here shownas being a greater frequency than frequency X. Therefore, when filter 10has responded to rewnant frequency X the complex impedance of filter Mhas not yet begun to change substantially and its output voltagemagnitude will remain at approximately the e, level, and conversely whenfilter ll has responded to resonant frequency Y, the complex impedanceof filter It) will have returned to approximately its stable value andthe output voltage magnitude will be at the e voltage level.

Referring now to H6. 4, there is shown a graph of the phase angle of theoutputvoltage of filter 10 in solid lines, and filter 11 in dottedlines. The graph has an abscissa representing increasing frequency, andan ordinate representing phase angle. From the graph it is apparent thatas the resonant frequency X of filter Ml is approached, its compleximpedance changes thereby changing the output voltage phase angle andcausing a 180 discontinuous phase change at the resonant frequency.Also, filter ll reacts in a like manner near resonant frequency Y.

lf resonant frequencies X and Y are properly chosen, a passband fromslightly below X to slightly above Y is obtained in the network asis'illustrated in FIG. 5. FIG. 5 depicts the output voltage magnitudefrom differential amplifier 17 as a function of frequency for a constantamplitude input signal at terminal M. The complex output voltage ofnotch filter 10 for a constant magnitude input signal can be representedby a phasor whose magnitude, at any particular frequency, is a point ofthe solid curve in FIG. 3 and whose phase angle, at that frequency, is apoint on the solid curve in H0. 4. The complex output voltage of notchfilter ll can be represented by a similar phasor. Differential amplifierl7 produces a network output voltage which is the difference of thosecomplex voltages. The magnitude of that network output voltage is shownin FIG. 5 and can be considered the response curve for the total filternetwork.

Referring now to FIG. 1, it can be seen that the outputs of filters iand 11 are connected to separate inputs to differential amplifier 17. Itis well known in the art that in differential amplifiers such as 17 adifference in voltage must appear between input terminals 18 and 19 foran output to appear at terminal 20. Referring to H68. 3 and it will beapparent that at frequencies well below X and well above Y, the compleximpedances of filters l0 and 11 are equal so their output voltagemagnitudes and phase angles are also equal, and thus there is nodifference voltage between input terminals l8 and 19 of amplifier 17.However, between a frequency slightly below resonant frequency X offilter l0, and a frequency slightly above resonant frequency Y of filter11, there is a band in which the magnitudes and the phase angles of theoutputs of filters l0 and 11 difier because their complex impedancesdiffer. During this time there will be a distinct difference in complexvoltages between input terminals l8 and 19 of amplifier 17 which resultsin an output at terminal 20. From FIG. 5, it can be seen that thenetwork output has maxima at frequencies X and Y because differentialamplifier. 17 receives a signal from only one filter. An attenuation ofthe network output signal occurs midway between frequencies X and Y andis increased as X and Y move farther apart. The curve shown in FIG. 5results when Y=2X.

Referring now to the operation of FIG. 2, those skilled in the art willrecognize the previously described components which make up the pair oftwin-T filters comparable to filters it) and 11 of FIG. 1. Field effecttransistors 40 and 60, along with resistors 43 and 63, respectively,have been added to the respective twin-T filter to perform abootstrapping operating on the outputs of the respective filter, in amanner known in the prior art. This bootstrapping is performed tosharpen up the amplitude and phase angle response curves of the twin-Tfilters. In response to an electrical signal at input terminal 16 ofFIG. 2, the output of the upper twin-T filter will be felt throughcapacitor 68 to appear on the base electrode of transistor 71), whilethe output of the lower twin-T filter will be felt through capacitor 69to appear on the base electrode of transistor 80. When the signals onthe base electrodes of transistors 70 and 30 are of equal magnitude andphase angle, there will be no difference voltage, and no output atterminal 20. However, when the electrical signal input at terminal 16has a frequency within the band where the notch filters have differentcomplex impedances the complex voltages applied to the base electrodesof transistors 70 and are not identical, so the resulting differentialvoltage produces an output signal at terminal 20. 7

An additional refinement is provided in each notch filter in FIG. 2 bythe addition of properly chosen resistors 46 and 66. Resistor 46 loadsone of the filters and resistor66 loads the other to adjust theircomplex impedances as a function of frequency and to obtain controlledskewing in the output voltage and phase angle curves. By proper skewing,attenuation of signals between frequencies X and Y can be reduced withsome loss of sharpness in signal attenuation at the edges of thepassband. Without such skewing, frequencies near the center of thepassband may be attenuated by a factor of 10 or more if Y is greaterthan 2X. Also, it is sometimes desireable to improve rejection of thenetwork at one frequency, or in a narrow band (e.g., 50-60 I-lz.) whichlies outside the primary passband. Proper loading of the filters byadjustment of the size of resistors 43 and 66 can provide such asupplementary rejection band by skewing the response curves of thefilters to provide a point at which the complex impedances of the twofilters cross over in value before either has become independent offrequency.

FIG. 6 illustrates an output voltage response curve 117, as a functionof frequency, which can be obtained from the circuit shown in FIG. 2. Itcan be seen that skewing has reduced attenuation near the center of thepassband and has produced a notch in the curve centered at frequency Z.Choice of loading values can position such a notch at either a higher orlower frequency than those within the primary passband.

It is apparent from the above discussion that the apparatus and methodof this invention can provide a desired output signal which will bepresent only during a selected frequency band, and be absent duringfrequencies above and below the band, the system or network being animprovement on susceptibility to unreliability or oscillation, andproviding a maximized differential voltage with a minimal insertion lossin the selected frequency band.

I claim:

1. A filter network comprising: a first electrical filter having aresonant frequency and having an input connection and an outputconnection; a second electrical filter, connected in parallel with thefirst electrical filter, having a resonant frequency approximatelydouble that of the first electrical filter and having an inputconnection and an output connection; single input means connected to theinput connection of the first electrical filter and o the inputconnection of the second electrical filter for rec eiving an electricalsignal; first high impedance means having an input connected to theoutput of the first electrical'filter and having an output terminal,

the first high impedance means for preserving the integrity of firsthigh'impedance means, a second input connected to the output of thesecond high impedance means, and having an output terminal, thedifferential amplifier subtracting the electrical signal from the firsthigh impedance means from the electrical signal from the second highimpedance means permitting, on the output terminal, the frequency rangedesired to pass.

1. A filter network comprising: a first electrical filter having aresonant frequency and having an input connection and an outputconnection; a second electrical filter, connected in parallel with thefirst electrical filter, having a resonant frequency approximatelydouble that of the first electrical filter and having an inputconnection and an output connection; single input means connected to theinput connection of the first electrical filter and to the inputconnection of the second electrical filter for receiving an electricalsignal; first high impedance means having an input connected to theoutput of the first electrical filter and having an output terminal, thefirst high impedance means for preserving the integrity of the inputelectrical signal that passes through the first electrical filter; asecond high impedance means having an input connected to the output ofthe second electrical filter and having an output terminal, the secondhigh impedance means for preserving the integrity of the inputelectrical signal that passes through the second electrical filter; anda differential amplifier having a first input connected to the output ofthe first high impedance means, a second input connected to the outputof the second high impedance means, and having an output terminal, thedifferential amplifier subtracting the electrical signal from the firsthigh impedance means from the electrical signal from the second highimpedance means permitting, on the output terminal, the frequency rangedesired to pass.